Solve for $x$ and $y$ using elimination. ${3x-6y = -9}$ ${x-5y = -21}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $-3$ ${3x-6y = -9}$ $-3x+15y = 63$ Add the top and bottom equations together. $9y = 54$ $\dfrac{9y}{{9}} = \dfrac{54}{{9}}$ ${y = 6}$ Now that you know ${y = 6}$ , plug it back into $\thinspace {3x-6y = -9}\thinspace$ to find $x$ ${3x - 6}{(6)}{= -9}$ $3x-36 = -9$ $3x-36{+36} = -9{+36}$ $3x = 27$ $\dfrac{3x}{{3}} = \dfrac{27}{{3}}$ ${x = 9}$ You can also plug ${y = 6}$ into $\thinspace {x-5y = -21}\thinspace$ and get the same answer for $x$ : ${x - 5}{(6)}{= -21}$ ${x = 9}$